I am preparing to build an 52" double swept wing Aeromaster with a Saito 90 for power but don't want that "huge" engine sticking up above the fuselage. I was thinking of mounting the engine horizontally and also mostly or fully enclose the engine in a cowling, To do that, I would offset the thrust line horizontally. The center of the crankshaft would be offset to the left by about an inch with perhaps no side thrust built in.
So, here is the question. Would that set up negatively affect the flying characteristics or have no affect at all?
I am curious to know your thoughts.

I'm not sure that the offset would be a factor but the lack of right thrust would and even more so with a large 4 stroke. Every time you pulled a vertical or entered a loop the airplane would want to veer left. Since you are scratch building, make the fuse wide enough to accommodate the width if the engine then offset the engine on the firewall 5/16" to the left and shim for 3 degrees of right thrust.

Any airplane in horizontal level flight must have all the forces and torques acting on the CG in perfect balance (one nulls the opposite).
If you extend the center-line of your shaft aft, the thrust of the engine combined with one inch of leverage over that CG (which is on the center line of the fuse seen from above) will create a yaw torque around that CG.

As the airplane yaws, a resistive torque will appear: the one created by the aerodynamic drag combined with some perpendicular distance of leverage over that CG.
In short, your plane will crab for high rpms of the engine, more for low speeds of the airplane, ....... or so I think.
Maybe you could experiment mixing some rudder and throttle.

In theory you are of course correct however we are talking about a model here. Would you be able to notice a slight, say 3 degree crab of an r/c model in flight? I know I wouldn't.

A one inch offset of the engine in this way would most certainly be noticeable in flight. Turns in one direction would be snappier than the other and if knife edge flying was tried the model would handle noticeably different from one side to the other. Even wing overs would be quite different from one to the other side.

In short don't do it. If you want to side mount the engine instead of inverted then add a Pitts style of cowl to the nose to cover the engine. The air from the cowl can exit the back along the side of the fuselage. That way you can mount the engine ON the centerline like it most definitely should be located.

And build in about 1.5 to 2 degrees of right thrust.

Keep in mind that the idea behind down and right thrust settings have been tested and proven time and again going back to before many of us were born. You ignore such "rules of thumb" at your own risk.

The crabbing may be slight ................ or not, depending on the power of the engine-prop, the air-speed of the model and the compensating rudder input: hard to estimate a priori.

An exaggerated comparison, but good to discuss off-center thrust and to show an interesting video: asymmetry is what makes a twin engine model difficult to control in a one-engine-out situation.

A good pilot in total control of a powerful rudder can reduce the emergency of such a situation:

http://www.youtube.com/watch?v=PftNh_SShlg

Thanks for the input. Not sure what I want to do. I was thinking that the offset would compensate for the lack of right thrust but further thinking makes me believe that offset isn't the same as right thrust. I might save myself a lot of aggravation and mount the engine inverted - with some right thrust.
Lnewqban- Thanks for the video. It brought back one of my most memorable events in my model flying. In the mid 70's, I was a member of an AMA Show Team and was doing an airshow where the star pilots were ? (can't bring up his name) with his Chipmunk, Joe Hughes with his 650 horse Stearman, the Red Devils, and Bob Hoover witht Shrike. The show team was to perform right after Hoover's flying performance so I set up my equipment off the edge of the runway by about 50 feet or so. At the end of his routine he did his engine off loops right in front of me. I had never seen Hoover do his show before and did not know what to expect. So, the engines were shot down and the Shrike came whistling down the runway toward me. Then, right in front of me he started to climb which was the start of his loop. I watched as he reached the apex of his loop and was somewhat startled as it appeared he had run out of airspeed and was sure to spin in. I moved away from the runway expecting the worst, but no, the Shrike was making it down the back-side of the loop. Relieved, I relaxed, but when I saw him enter a second loop deadstick, I was sure he was going down. But, again all was well. Fear set in again as I watched him come out of the loop and proceed to do a roll before he set up his landing. Afterwards, I realized he might have been using me as a reference point for his loops as the bottom of the loops were squarly in front of me. Now in today's legal world, that might not have been allowed as I was very close to the action, but what a thrill it was.
Any additional thought on the offset, would be welcome, and I am sure, interesting.

You are welcome

There is a documentary film about Hoover in the making:

http://www.thebobhooverproject.com/

Regarding the off-set, it would be interesting to experiment with it if you could install the engine provisionally without the cowl.